A distribution element intended to be fixed to a support structure for supplying cooling fluid to a wall to be cooled facing the distribution element, the distribution element including a body defining a cooling fluid distribution internal volume and a multi-perforated plate which delimits the internal volume and includes a plurality of outlet through-perforations which put the cooling fluid distribution internal volume into communication with the wall to be cooled, the distribution element including an inlet orifice opening into the cooling fluid distribution internal volume, wherein for directing the cooling fluid from the inlet orifice to the plurality of outlet through-perforations the cooling fluid distribution internal volume includes directional fins.